Question

Point b on a segment with endpoints a(2, -1) and c(4, 2) partitions the segment in a 1:3 ratio. Find the coordinates of point b.

1) (0.5, 0.75)
2) (-0.25, 2.5)
3) (0.75, 0.5)
4) (2.5, -0.25)

Answer 1

To find the coordinates of point b, we need to find the point that divides the segment in a 1:3 ratio. Using the midpoint formula, we can find the coordinates of the midpoint between points a and c. Then, we use the ratios to find the coordinates of point b.

Step-by-step explanation:

To find the coordinates of point b, we need to find the point that divides the segment in a 1:3 ratio. The ratio tells us that the distance from point a to point b is one-third of the distance from point a to point c. Using the midpoint formula, we can find the coordinates of point b.

First, find the coordinates of the midpoint between points a and c:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Midpoint = ((2 + 4) / 2, (-1 + 2) / 2)

Midpoint = (3, 0.5)

Now, we need to find the coordinates of point b, which is one-third of the way from the midpoint to point c:

x-coordinate of b = (2/3) * (x-coordinate of midpoint) + (1/3) * (x-coordinate of c)

x-coordinate of b = (2/3) * 3 + (1/3) * 4

x-coordinate of b = 2 + 1.3333

x-coordinate of b = 3.3333

y-coordinate of b = (2/3) * (y-coordinate of midpoint) + (1/3) * (y-coordinate of c)

y-coordinate of b = (2/3) * 0.5 + (1/3) * 2

y-coordinate of b = 0.3333 + 0.6666

y-coordinate of b = 1

Therefore, the coordinates of point b are (3.3333, 1). None of the given answer choices match this, so the correct answer is not provided.